Field of the Invention
The invention relates to a method for determining a radial k-space trajectory for a magnetic resonance (MR) control sequence, and to an MR control sequence having a radial k-space trajectory. The invention furthermore relates to a method for operating a magnetic resonance system. The invention additionally relates to an MR control sequence having a radial k-space trajectory. The invention also relates to a control sequence determination device for determining a radial k-space trajectory of an MR control sequence. The invention further relates to a magnetic resonance system.
Description of the Prior Art
Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a technique in which the inflow of a contrast agent into a tissue that is to be examined is observed as a function of time. During this process, multiple image datasets of the tissue that is to be examined are calculated at different times. The optimal times are not known in advance because the time between injection of the contrast agent and arrival of the contrast agent in the target tissue varies according to patient.
Various methods have been developed in conventional dynamic MR imaging in order to synchronize the acquisition of the contrast-determining k-space regions with the arrival of the contrast agent in the target tissue during the sampling or readout of raw data. They include starting the measurement based on empirical values, additional test measurements in order to determine the arrival time, and real-time sequences for detecting the arrival in an afferent vessel. Each of these methods has advantages and disadvantages.
Radial imaging with a temporal variation of the projection angles that are based on the golden section permits the times at which images are reconstructed to be specified only after the data acquisition, and it therefore gets by without the aforementioned methods. The advantage achieved by means of the radial acquisition technique is that each spoke acquires information from the contrast-determining central k-space regions. Such an approach is illustrated in FIG. 2. In conventional Cartesian imaging, however, the central rows determining the contrast are acquired at a specific time instant during the measurement. Incrementing the azimuthal spoke angle of 111.25° (known as the golden angle) between spokes succeeding one another in time allows an arbitrary window of Nw sequentially measured spokes to be achieved that covers k-space approximately uniformly, and as a result an isotropically resolved image can be calculated from the spokes belonging to the window. The golden angle in the unit radians (unit symbol: rad) is yielded from the quotient of the number it and the golden number
  γ  =                              5                +        1            2        .  In this case the golden number results from the quotient a/b of a line segment having the subsegments a and b which is divided by the golden section.
In non-dynamic radial imaging, in contrast, a total number N of spokes is initially determined in such a way that N azimuthally uniformly distributed spokes just cover k-space of a desired size (i.e. a desired amount of k-space) sufficiently in accordance with the Nyquist-Shannon theorem. Accordingly, an angular increment dΦ=π/N between adjacent spokes in k-space is specified by the number N. The increment dΦ is e.g. likewise chosen as the angular increment between spokes measured sequentially in time, such that k-space is uniformly and adequately covered after precisely N profiles.
In early dynamic radial methods, the k-space was acquired in n cycles. Within each cycle, the angle between successively measured spokes was incremented by n·dΦ each time. The number of time instants at which isotropically resolved images can be calculated is increased by a factor n as a result. However, the full flexibility of the golden scheme in respect of the choice of the time windows is not achieved by that means. Such a method is illustrated in FIG. 1.
However, the golden angle as angular increment is also associated with a series of disadvantages compared to the angular increment dΦ. The most serious of said disadvantages is that the number of spokes required when using the golden angle scheme in order to cover k-space of a given size just sufficiently in accordance with the Nyquist-Shannon sampling theorem is generally substantially greater than the corresponding number of spokes when using a scheme having a constant angular increment between adjacent spokes in the k-space. The actual number of spokes N used for the reconstruction of an image determines the temporal resolution of the dynamic technique. Thus, if the number of spokes N is chosen such that k-space is just sufficiently covered according to the Nyquist-Shannon sampling theorem, then the temporal resolution decreases when using the golden angle scheme compared to the temporal resolution when using a scheme having a constant angular increment between adjacent spokes in the k-space. It is frequently the case in dynamic imaging that images are calculated from time windows which are too short for acquiring the number of spokes required by the Nyquist-Shannon sampling theorem in order to achieve a desired temporal resolution. In this case the degree of undersampling when using the golden angle scheme is greater than when using a scheme having a constant angular increment between adjacent spokes in the k-space. Accordingly, artifacts in consequence of the undersampling are therefore worse.